The present invention relates to an adsorption reactor and an adsorption method for removing SO.sub.2 from waste gases. During adsorptive removal of SO.sub.2 from waste gases with the aid of the above mentioned adsorption reactors, the separation degree of SO.sub.2 is improved by reducing the temperature of the waste gases to, for example, below 120.degree. C. It has been tried to introduce cold fluid into the waste gas prior to its entrance into the adsorption reactor. Such a method has the disadvantage that it involves increase of the volume of the gas and also wrong utilization of the heat content of the waste gases. A further problem is that the waste gas, prior to the entrance into the adsorption medium bed, must have always sufficiently high temperatures for avoiding corrosion by falling below the dew point of sulfuric acid. Thus, there are two contradicting requirements as to the temperature supply in or prior to adsorption reactors. It has been shown that during the above mentioned introduction of a fluid before the adsorption medium bed no adsorption problem takes place. However, the introduction for example of water in the waste gas prior to the entrance into an adsorption reactor filled with carbonaceous adsorption medium under favorable conditions, for example complete evaporation, temperatures below 110.degree.-120.degree. C. cannot be attained (see R. Noack, K. Knoblauch, VDI-Berichte No. 267 (1976), pages 37-42).